OFFSET
1,2
COMMENTS
a(n)=n if n is prime. - Robert Israel, Sep 17 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{p|n, q|n, p and q prime, p<=q} p.
EXAMPLE
a(6) = 7; There are 2 prime divisors of 6: {2,3}. If we list all of the ordered pairs (p,q) with p<=q, we get (2,2), (2,3) and (3,3). The sum of the first coordinates from each pair is 2 + 2 + 3 = 7.
a(10) = 9; There are 2 prime divisors of 10: {2,5}. If we list all of the ordered pairs (p,q) with p<=q, we get (2,2), (2,5) and (5,5). The sum of the first coordinates from each pair is 2 + 2 + 5 = 9.
MAPLE
f:= proc(n) local F, i, j;
F:= sort(convert(numtheory:-factorset(n), list), `>`);
add(i*F[i], i=1..nops(F))
end proc:
map(f, [$1..100]); # Robert Israel, Sep 17 2020
PROG
(PARI) a(n) = my(vp = factor(n)[, 1]~); sum(iq=1, #vp, sum(ip=1, iq, vp[ip])); \\ Michel Marcus, Aug 21 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 20 2020
STATUS
approved